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Unbiased estimation of the parameter of a selected binomial population
Authors:Linda Tappin
Affiliation:Montclair State College , Upper Montclair, New Jersey, 07043
Abstract:
The problem is to estimate the parameter of a selected binomial population. The selction rule is to choose the population with the greatest number of successes and, in the case of a tie, to follow one of two schemes: either choose the population with the smallest index or randomize among the tied populations. Since no unbiased estimator exists in the above case, we employ a second stage of sampling and take additional observations on the selected population. We find the uniformly minimum variance unbiased estimator (UMVUE) under the first tie break scheme and we prove that no UMVUE exists under the second. We find an unbiased estimator with desirable properties in the case where no UMVUE exists.
Keywords:unbiased estimation  estimation after selection  umvu estimator  minimax
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